Did this route for years and there are limitless options but the quickest is up Dog kennel Hill and take the main road through Camberwell and on to Vauxhall Bridge, then along the Embankment and it doesn't particularly matter which right turn you take then up to Hammersmith. it will depend exactly where you need to go. There are some lovely variations - including the 'four parks' route that takes in Dulwich park, Brockwell park, Battersea Park and Brmopton cemetery. Adds about 10 mins but lovely. Whatever route you do it will be quicker than public transport.